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# Magic Square

Input: Standard Input (stdin)
Output: Standard Output (stdout)
Memory limit: 256 megabytes
Time limit: 1.0 seconds

A magic square is a square grid of numbers where the sums of each row, column, and both diagonals are the same.

You will be given a 3x3 magic square of positive integers. However, the magic square is incomplete – there are $N$ missing elements, denoted by the value $0$.

Solve the magic square.

## Input

There will be three lines, each containing three space-separated integers, representing elements of the incomplete magic square.

Exactly $N$ of the elements will be $0$, indicating a missing value that must be found. All remaining elements will be between $1$ and $10\,000$ (inclusive).

## Output

You should print three lines, each containing three space-separated integers, representing elements of the completed magic square.

It is guaranteed that there is a unique solution, and that all elements of the solution will be between $1$ and $10\,000$ (inclusive).

• Subtask 1 (25%): $N = 1$
• Subtask 2 (25%): $1 \le N \le 2$
• Subtask 3 (25%): $1 \le N \le 3$
• Subtask 4 (25%): $1 \le N \le 5$
• ### Sample Input 1

3 3 6
7 0 1
2 5 5


### Sample Output 1

3 3 6
7 4 1
2 5 5

• ### Sample Input 2

6 1 0
7 0 3
0 9 4


### Sample Output 2

6 1 8
7 5 3
2 9 4